Just in terms of ones near(ish) Southampton, depending on what exactly you're counting as a railway museum, I can think of the Mid-Hants Railway, Isle of Wight Steam Railway, Swanage Railway, Hayling Light Railway, North Dorset Railway, Amberley Museum, Milestones Museum, Didcot Railway Centre, and STEAM (Swindon). Of those, I'd call the first five preserved, heritage or other private railways*, the next two museums with trains (well, a train and tram, for Milestones), and the last two proper railway museums.
*From memory, Mid-Hants has some sort of museum or workshop viewing area; I'm unsure for the others.